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Diplomarbeit / Master Thesis
Simulation of Capillary Microcirculation for Computation of Interstitial Hydrostatic Pressure
Supervision:
Background:
Microcirculation plays a fundamental role in living organism. It is through microcirculation that living
cells' nutritional and respiratory needs are met and cellular waste products are eliminated.
Thus building effective computational models of microcirculation is of great importance for medical research.
Incoming molecules, nutrients and oxygen are transported from the arterial end
of capillaries through the interstitial space and into the surrounding cells.
Following a somewhat reverse path, cellular waste products are eliminated from the
cells through the interstitial space and into the venous end of the capillaries.
Thus the capillary is the principal site of exchange in the organism (see left Figure below).
The embedded lymphatic network plays a physiologically crucial role in both immune function and the
maintenance of tissue interstitial fluid balance through the transport of interstitial fluid back to the
blood circulation.
The objective of this project is to build a 3D computational model that generalizes starling's law of microcirculation.
This law describes the movement of fluid across capillary membranes due to hydrostatic and oncotic forces.
In this regard, normal and pathological states will be modelled.
Pathological conditions include an increase in venous blood hydrostatic pressure or a reduction of the blood colloid osmotic pressure.
These may lead to the accumulation of interstitial fluid and thus to the formation of oedema.
Tasks:
The task in this thesis is to model capillary microcirculation and to simulate the relation between
hydrostatic pressures in vessels and in interstitial space (oncotic pressures will be investigated in a future thesis).
The simulation will be embedded into the
waLBerla
framework, which is based on an all-in-one Lattice-Boltzmann solver and provides support for a wide range of applications.
This includes:
- Simulation of blood flow in vessels by means of the lattice Boltzman method (LBM)
- Modelling of interstitium as porous medium by Darcy's law (describes relation between flux and pressure)
- Coupling of both methods by means of suitable boundary conditions on vessel walls, describing pressure drop
- Output of pressure and fluid velocity in the computational domain
As a first step, the flow in the artery, as well as the pressure drop across the artery wall should be modelled.
Later, the reabsorption of the fluid by the veins can be added. Finally, the drainage (and corresponding pressure
decrease) by the lymph can be modelled and computed.
For the blood flow simulation in vessels, an existing model can be applied [1].
Additionally, there is already a solver for partial differential equations (PDEs) available that can be used for solving Darcy's law.
Recommended knowledge:
- Basic knowledge in computational fluid dynamics and PDE solvers
- Advanced C++ programming
- Interest in simulation and modelling of biophysical phenomena
Status:
Free
References:
[1] Jan Götz: Numerical Simulation of Blood Flow using the Lattice Boltzmann method,
July 2006
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